Steady-state analysis of a multiserver queue in the Halfin-Whitt regime

By David Gamarnik, Petar Momcilovic. Advances in Applied Probability, 2007

59 citations recorded by the source corpus.

We consider a multiserver queue in the Halfin-Whitt regime: as the number of servers n grows without a bound, the utilization approaches 1 from below at the rate Assuming that the service time distribution is lattice valued with a finite support, we characterize the limiting scaled stationary queue length distribution in terms of the stationary distribution of an explicitly constructed Markov chain. Furthermore, we obtain an explicit expression for the critical exponent for the moment generating function of a limiting stationary queue length. This exponent has a compact representation in terms of three parameters: the amount of spare capacity and the coefficients of variation of interarrival and service times. Interestingly, it matches an analogous exponent corresponding to a single-server queue in the conventional heavy-traffic regime.

Subfields: Computer Networks and Communications, Management Information Systems, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/f7c1ebd0d6d1bf2b566404ab53ae3b88ff18500c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Networks and Communications

1. Josh E. Reed
2. J. Dai
3. Tolga Tezcan
4. Haya Kaspi
5. Kavita Ramanan
6. Shuangchi He
7. Weining Kang

In Management Information Systems

1. Kavita Ramanan
2. Haya Kaspi
3. Weining Kang
4. Josh E. Reed
5. J. Dai
6. Tolga Tezcan
7. Shuangchi He
8. Ward Whitt

In Management Science and Operations Research

1. Kavita Ramanan
2. Haya Kaspi
3. Weining Kang
4. Josh E. Reed
5. J. Dai
6. Tolga Tezcan
7. Shuangchi He
8. Ward Whitt

Citations in the corpus

• Asymptotic approximations for stationary distributions of many-server queues with abandonment (2010, background): “For a many-server queue with stationary renewal arrivals, a finitely supported, lattice-valued service time distribution and no abandonments, in the so-called Halfin–Whitt asymptotic regime where the number of servers N goes to infinity and the corresponding arrival rate grows as N − β√N for some β ”
• The G/GI/N queue in the Halfin–Whitt regime (2009, background): “The Annals of Applied Probability 2009, Vol. 19, No. 6, 2211–2269 DOI: 10.1214/09-AAP609 © Institute of Mathematical Statistics, 2009 THE G/GI/N QUEUE IN THE HALFIN–WHITT REGIME1 BY JOSH REED”
• SPDE Limits of Many Server Queues (2010, methodology): “In addition to the process level results described above, under the stability assumption β > 0, results on the asymptotics of steady state distributions in the Halfin–Whitt regime have been obtained by Jelenkovic, Mandelbaum and Momçilović [18] for deterministic service times and by Gamarnik and Mo”
• Many-server diffusion limits for G/Ph/n+GI queues (2010, methodology): “Since yn! y as n!1 in the standard J1 topology on DK+1, it follows from Proposition 3.5.3 of Ethier and Kurtz (1986) that there exists a sequencef ng such that”
• Positive recurrence of piecewise Ornstein–Uhlenbeck processes and common quadratic Lyapunov functions (2011, background): “Although quadratic Lyapunov functions are ubiquitous in the literature on queueing systems Dai and Prabhakar (2000), Gamarnik and Momčilović (2008), Tassiulas and Ephremides (1992), to our knowledge, our paper is the first to exploit CQLFs in this context.”